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Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination

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  • Chang-Song Deng

    (Wuhan University)

Abstract

In this paper, we are concerned with the subgeometric rate of convergence of a Markov chain with discrete-time parameter to its invariant measure in the f-norm. We clarify how three typical subgeometric rates of convergence are inherited under a discrete-time version of Bochner’s subordination. The crucial point is to establish the corresponding moment estimates for discrete-time subordinators under some reasonable conditions on the underlying Bernstein function.

Suggested Citation

  • Chang-Song Deng, 2020. "Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination," Journal of Theoretical Probability, Springer, vol. 33(1), pages 522-532, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-019-00879-z
    DOI: 10.1007/s10959-019-00879-z
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    References listed on IDEAS

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    1. Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    2. Bendikov, Alexander & Cygan, Wojciech & Trojan, Bartosz, 2017. "Limit theorems for random walks," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3268-3290.
    3. Alexander Bendikov & Wojciech Cygan, 2015. "On massive sets for subordinated random walks," Mathematische Nachrichten, Wiley Blackwell, vol. 288(8-9), pages 841-853, June.
    Full references (including those not matched with items on IDEAS)

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